Abstract

In this paper, we investigate a constrained formulation of neural networks where the output is a convex function of the input. We show that the convexity constraints can be enforced on both fully connected and convolutional layers, making them applicable to most architectures. The convexity constraints include restricting the weights (for all but the first layer) to be non-negative and using a non-decreasing convex activation function. Albeit simple, these constraints have profound implications on the generalization abilities of the network. We draw three valuable insights: (a) Input Output Convex Networks (IOC-NN) self regularize and almost uproot the problem of overfitting; (b) Although heavily constrained, they come close to the performance of the base architectures; and (c) The ensemble of convex networks can match or outperform the non convex counterparts. We demonstrate the efficacy of the proposed idea using thorough experiments and ablation studies on MNIST, CIFAR10, and CIFAR100 datasets with three different neural network architectures. The code for this project is publicly available at: https://github.com/sarathsp1729/Convex-Networks.

Abstract

Complete information about the class label is not given in many real-world classification problems. For example in a multiclass setting, instead of the ground-truth label, we can be given a set of candidate labels, assuming that the true label belongs to this set. This type of setting is called learning under partial labels. In this paper, we propose exact passive-aggressive online algorithms for multiclass classification using only partial labels. For updating the weights, we find the exact solution of a quadratic optimization problem under multiple class separability constraints. We obtain this by finding the active constraints using KKT conditions of the optimization problem. The set of support classes for which the weight vector is to be updated is determined by these constraints. The proposed algorithms are called PA, PA-I, and PA-II. We also provide a thorough theoretical analysis of the proposed algorithms including regret bounds. We provide extensive simulation results to show the effectiveness of the proposed approaches.

Abstract

This paper introduces a new online learning framework for multiclass classification called learning with diluted bandit feedback. At every time step, the algorithm predicts a candidate label set instead of a single label for the observed example. It then receives feedback from the environment whether the actual label lies in this candidate label set or not. This feedback is called "diluted bandit feedback". Learning in this setting is even more challenging than the bandit feedback setting, as there is more uncertainty in the supervision. We propose an algorithm for multiclass classification using dilute bandit feedback (MC-DBF), which uses the exploration-exploitation strategy to predict the candidate set in each trial. We show that the proposed algorithm achieves O(T^{1-frac{1}{m+2}}) mistake bound if candidate label set size (in each step) is m. We demonstrate the effectiveness of the proposed approach with extensive simulations.

Abstract

No Results Found

Abstract

In this paper, we propose deep architectures for learning instance specific abstain (reject option) binary classifiers. The proposed approach uses double sigmoid loss function as described by Kulin Shah and Naresh Manwani in (" Online Active Learning of Reject Option Classifiers", AAAI, 2020), as a performance measure. We show that the double sigmoid loss is classification calibrated. We also show that the excess risk of 0-d-1 loss is upper bounded by the excess risk of double sigmoid loss. We derive the generalization error bounds for the proposed architecture for reject option classifiers. To show the effectiveness of the proposed approach, we experiment with several real world datasets. We observe that the proposed approach not only performs comparable to the state-of-the-art approaches, it is also robust against label noise. We also provide visualizations to observe the important features learned by the network corresponding to the abstaining decision.

Abstract

This paper addresses the problem of multiclass classification with corrupted or noisy bandit feedback. In this setting, the learner may not receive true feedback. Instead, it receives feedback that has been flipped with some non-zero probability. We propose a novel approach to deal with noisy bandit feedback based on the unbiased estimator technique. We further offer a method that can efficiently estimate the noise rates, thus providing an end-to-end framework. The proposed algorithm enjoys a mistake bound of the order of O(√T ) in the high noise case and of the order of O(T 2/3) in the worst case. We show our approach’s effectiveness using extensive experiments on several benchmark datasets.

Abstract

No Results Found

Abstract

Active learning is an important technique to reduce the number of labeled examples in supervised learning. Active learning for binary classification has been well addressed in machine learning. However, active learning of the reject option classifier remains unaddressed. In this paper, we propose novel algorithms for active learning of reject option classifiers. We develop an active learning algorithm using double ramp loss function. We provide mistake bounds for this algorithm. We also propose a new loss function called double sigmoid loss function for reject option and corresponding active learning algorithm. We offer a convergence guarantee for this algorithm. We provide extensive experimental results to show the effectiveness of the proposed algorithms. The proposed algorithms efficiently reduce the number of label examples required.

Abstract

This paper addresses the problem of multiclass classification with corrupted or noisy bandit feedback. In this setting, the learner may not receive true feedback. Instead, it receives feedback that has been flipped with some non-zero probability. We propose a novel approach to deal with noisy bandit feedback, based on the unbiased estimator technique. We further propose an approach that can efficiently estimate the noise rates, and thus providing an end-to-end framework. The proposed algorithm enjoys mistake bound of the order of O(√T). We provide a theoretical mistake bound for our proposal. We also carry out extensive experiments on several benchmark datasets to demonstrate that our proposed approach successfully learns the underlying classifier even using noisy bandit feedbacks.

Abstract

In this paper, we propose online algorithms for multiclass classification using partial labels. We propose two variants of Perceptron called Avg Perceptron and Max Perceptron to deal with the partially labeled data. We also propose Avg Pegasos and Max Pegasos, which are extensions of the Pegasos algorithm. We also provide mistake bounds for Avg Perceptron and regret bound for Avg Pegasos. We show the effectiveness of the proposed approaches by experimenting on various datasets and comparing them with the standard Perceptron and Pegasos.